Answer:
B) 1 < x < 13
Step-by-step explanation:
use triangle inequality theorem which states that the sum of any two sides must be greater than the third side
let x = third side
6 + 7 > x; x < 13
6 + x > 7; x > 1
x + 7 > 6; x > -1
there will always be one inequality which produces a negative value which you can exclude from your answer because a length cannot be negative
I assume you're just solving for x. Factorize the left side as
3 sin²(x) - 3 sin⁴(x) = 3 sin²(x) (1 - sin²(x)) = 0
Recall that
sin²(x) + cos²(x) = 1
so that the equation further reduces to
3 sin²(x) cos²(x) = 0
Also recall the double angle identity,
sin(2x) = 2 sin(x) cos(x)
which lets us rewrite the equation as
3/2² (2 sin(x) cos(x))² = 3/4 sin²(2x) = 0
Solve for x :
3/4 sin²(2x) = 0
sin²(2x) = 0
sin(2x) = 0
2x = arcsin(0) + 2nπ or 2x = π - arcsin(0) + 2nπ
(where n is any integer)
2x = 2nπ or 2x = (2n + 1) π
x = nπ or x = (2n + 1)/2 π
Notice that this means the solution set is
{…, -2π, -3π/2, -π, -π/2, 0, π/2, π, 3π/2, 3π, …}
so we can condense the solution further to
x = nπ/2
with any integer n.
Answer:
6*12=72
Step-by-step explanation:
Find the factors of 72 and see which ones are double it's pair.
The answer will be -12, as the '| |' Part means it will ALWAYS BE POSITIVE. However, the negative is on the outside of the lines, so all you really need to do is drop the lines to get -12 as your answer.
Circumference is the same as perimeter
